Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#21181 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #121 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| socle | C22×C19 | C2×#121 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C23×C4×C19 ◁ G | |
874 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22)(24,25)(26,36)(27,41)(28,33)(29,34)(30,35)(31,39)(32,43)(37,51)(38,46)(40,49)(42,48)(44,47)(45,54)(50,53)(52,55);(20,22,23,21)(24,26)(25,31)(27,37)(28,38)(29,39)(30,40)(32,45)(33,36)(34,49)(35,46)(41,50)(42,52)(43,53)(44,54)(47,55)(48,51);(24,27,29,43,30,44,28,42)(25,32,33,41,35,48,34,47)(26,37,39,53,40,54,38,52)(31,45,36,50,46,51,49,55);(24,28,30,29)(25,33,35,34)(26,38,40,39)(27,42,44,43)(31,36,46,49)(32,41,48,47)(37,52,54,53)(45,50,51,55)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14169);